Final answer:
The limit of the given expression is -6.
Step-by-step explanation:
To find the limit of the given expression, we can use L'Hôpital's Rule. Let's differentiate the numerator and denominator separately:
f(2) = 4
f'(2) = 4
lim(x→2) [xf(2)−2f(x)/(x−2)] = lim(x→2) [f(2) + x*f'(2) - 2f(x)]/(x-2)
Substituting the given values, we have:
lim(x→2) [4 + 2x - 2f(x)]/(x-2)
Now, let's apply L'Hôpital's Rule by differentiating the numerator and denominator again:
lim(x→2) [2 - 2f'(x)] = 2 - 2f'(2) = 2 - 2(4) = -6